High quality factor MEMS silicon flower-of-life vibratory gyroscope

ABSTRACT

A resonator includes an anchor, an outer stiffener ring on an outer perimeter of the resonator, and a plurality of curved springs between the anchor and the outer stiffener ring.

CROSS REFERENCE TO RELATED APPLICATIONS

This application relates to and claims the benefit of priority from U.S.Provisional Patent Application 62/542,744, filed Aug. 8, 2017, which isincorporated herein by reference as though set forth in full.

STATEMENT REGARDING FEDERAL FUNDING

None.

TECHNICAL FIELD

This disclosure relates to resonators and gyroscopes, and in particularvibratory gyroscopes.

BACKGROUND

Prior art vibratory gyroscopes include silicon disk resonator gyroscopes(DRGs), and example prior art silicon DRGs are described in U.S. Pat.No. 6,944,931B2, issued Sep. 20, 2005 and U.S. Pat. No. 7,040,163B2,issued May 9, 2006, which are incorporated herein by reference. Theseprior art silicon DRGs may have resonance frequencies of around 14 kHzand Q-factors of around 80,000. DRGs are sensitive to vibration, shock,and temperature. Also due to their natural frequency, silicon DRGs donot operate well under harsh vibration and thermal conditions. To reducethese vibration, shock, and temperature effects, prior art DRGs requirean undesirable size, weight and volume to provide some mitigation.

What is needed is an improved vibratory gyroscope that has an attractiveCSWaP (Cost Size Weight and Power), a higher resonance frequency and ahigher Q-factor and which is less sensitive to vibration, shock, andtemperature. The embodiments of the present disclosure answer these andother needs.

SUMMARY

In a first embodiment disclosed herein, a resonator comprises an anchor,an outer stiffener ring on an outer perimeter of the resonator, and aplurality of curved springs between the anchor and the outer stiffenerring.

In one aspect the outer stiffener ring has a first diameter and theanchor is concentric with the outer stiffener ring and has a seconddiameter less than the first diameter.

In another aspect the resonator further comprises at least one innerstiffener ring concentric with the outer stiffener ring, wherein theplurality of curved springs are coupled to the at least one innerstiffener ring, and wherein the outer stiffener ring has a firstdiameter that is greater than a second diameter of the inner stiffenerring.

In yet another aspect the plurality of curved springs comprise a firstset of springs each having a clockwise curvature between the anchor andthe outer stiffener ring, and a second set of curved springs each havinga counter-clockwise curvature between the anchor and the outer stiffenerring.

In still another aspect the plurality of curved springs comprise a firstset of curved springs each having a convex curvature between the anchorand the outer stiffener ring, and a second set of curved springs eachhaving a concave curvature between the anchor and the outer stiffenerring, and the plurality of curved springs are arranged between theanchor and the outer stiffener ring such that a respective spring havinga convex curvature intersects a respective spring having a concavecurvature at a same location on the inner stiffener.

In another aspect the outer stiffener ring has a diameter ranging from 1to 20 millimeters, the anchor has a diameter ranging from 0.1-10millimeters, the outer stiffener ring has a width ranging from 1-500micrometers, the plurality of springs have a width ranging from 1-500micrometers, and the resonator has a thickness ranging from 10-500micrometers.

In another aspect the outer stiffener ring has an aspect ratio rangingfrom 1:500 to 50:1, wherein the aspect ratio is the ratio of the widthto the thickness of the outer stiffener ring, the plurality of curvedsprings with an aspect ratio ranging from 1:500 to 50:1, wherein theaspect ratio is the ratio of the width to the thickness of the springs.

In another aspect the plurality of curved springs have a rotationalsymmetry about a center axis with an N fold of symmetry, where N is apositive integer.

In another aspect, the resonator comprises a plurality of innerstiffener rings each concentric with the outer stiffener ring, wherein apitch between each adjacent inner stiffener ring, or between the outerstiffener ring and a respective inner stiffener ring adjacent to theouter stiffener ring, or between the anchor and a respective innerstiffener ring adjacent to the anchor is the same.

In another aspect, the resonator comprises a plurality of electrodesoutside the outer perimeter of the resonator, wherein the plurality ofelectrodes are not in physical contact with the outer stiffener ring,and wherein a gap is between each electrode and the outer stiffenerring.

In another aspect, the gap is filled with a gas or a vacuum.

In another aspect, the resonator comprises a plurality of internalelectrodes, wherein each internal electrode is located between a curvedspring and another curved spring and the at least one inner stiffenerring, or between a curved spring and another curved and the anchor, orbetween a curved spring and another curved and the outer stiffener ring,wherein the plurality of inner electrodes are not in physical contactwith the curved springs, the inner stiffener ring, the anchor or theouter stiffener ring, and wherein a gap is between each inner electrodeand adjacent curved springs, the at least one inner stiffener ring, theanchor and the outer stiffener ring.

In another aspect, the resonator has a thermoelastic damping limitedquality factor (QTED) greater than 150,000.

In another aspect, the resonator has a resonance frequency greater than30 kHz.

In another aspect, the resonator comprises silicon-on-insulator (SOI).

In another aspect, the resonator comprises silicon, quartz, or SiC.

In another aspect, a thermoelastic damping limited quality factor (QTED)and a resonance frequency of the resonator increases with increasingwidth of the curved springs.

In another aspect, the outer stiffener ring has a width greater than awidth of each of the curved springs.

In another aspect, the plurality of curved springs comprise a pluralityof convex springs coupled to the outer stiffener ring and pointingtowards the anchor.

In another aspect, the plurality of curved springs comprise a pluralityof convex springs coupled to the anchor and pointing towards the outerstiffener ring.

In another embodiment disclosed herein, a resonator comprises an anchor,an outer stiffener ring on an outer perimeter of the resonator, and aplurality of curved springs organized in a flower-of-life pattern.

In one aspect, the flower-of-life pattern is configured by overlappedcurved springs that form outlines of leaf shapes, wherein the outlinesof the leaf shapes formed include but not limited to linear, elliptical,oval, ovate, deltoid, cordate, oblong, rhomboid, obovate, oblanceolate,orbicular, lanceolate, reniform, spathulate outlines, or combinationsthereof, wherein the outline of leaf shapes formed are symmetric andsymmetrically arranged around the anchor, wherein the flower-of-lifepattern has a rotational symmetry about a center axis with N fold ofsymmetry, where N is a positive integer.

In another embodiment disclosed herein, a method of providing aresonator comprises providing a silicon-on-insulator (SOI) wafercomprising an insulator with backside silicon on one side of theinsulator and front side silicon on another side of the insulator,patterning a front side alignment target on the front side silicon,depositing and patterning front side metal on the front side silicon,patterning the front side silicon using deep reactive ion etching toexpose the insulator and to form an anchor, an outer stiffener ring onan outer perimeter of the resonator, and a plurality of curved springscoupled between the anchor and the outer stiffener ring, removing aportion of the insulator by using an etchant to undercut and release aresonant portion of the resonator from the backside silicon, and leavingan anchor portion of the resonator attached to the backside silicon.Patterning can be a form of etching or depositing.

In one aspect the method further comprises patterning a backsidealignment target on the backside silicon, and depositing and patterningbackside metal on the backside silicon for attachment to a package.Patterning can be a form of etching or depositing.

In another aspect depositing and patterning front side metal on thefront side silicon comprises depositing metal for electrical contact toan electrode and for electrical contact to the anchor.

In another aspect the insulator is silicon dioxide (SiO₂), and theetchant is hydrofluoric acid (HF).

In another aspect the outer stiffener ring has a first diameter, and theanchor is concentric with the outer stiffener ring and has a seconddiameter less than the first diameter.

In another aspect patterning the front side silicon using deep reactiveion etching further comprises patterning to form at least one innerstiffener ring concentric with the outer stiffener ring, wherein theplurality of curved springs are coupled to the at least one innerstiffener ring, and wherein the outer stiffener ring has a firstdiameter that is greater than a second diameter of the inner stiffenerring. Wherein patterning can be a form of etching or depositing.

In another aspect the plurality of curved springs comprise a first setof springs each having a clockwise curvature between the anchor and theouter stiffener ring, and a second set of curved springs each having acounter-clockwise curvature between the anchor and the outer stiffenerring.

In another aspect the plurality of curved springs comprise a first setof curved springs each having a convex curvature between the anchor andthe outer stiffener ring, and a second set of curved springs each havinga concave curvature between the anchor and the outer stiffener ring; andthe plurality of curved springs are arranged between the anchor and theouter stiffener ring such that a respective spring having a convexcurvature intersects a respective spring having a concave curvature at asame location on the inner stiffener.

In another aspect the outer stiffener ring has a diameter ranging from 1to 20 millimeters, the anchor has a diameter ranging from 0.1-10millimeters, the outer stiffener ring has a width ranging from 1-500micrometers, and the resonator has a thickness ranging from 10-500micrometers.

In another aspect the plurality of curved springs have a rotationalsymmetry about a center axis with an N fold of symmetry, where N is apositive integer.

In another aspect the method further comprises patterning a plurality ofinner stiffener rings each concentric with the outer stiffener ring,wherein a pitch between each adjacent inner stiffener ring, or betweenthe outer stiffener ring and a respective inner stiffener ring adjacentto the outer stiffener ring, or between the anchor and a respectiveinner stiffener ring adjacent to the anchor is the same. Patterning canbe a form of etching or depositing.

In another aspect the method further comprises forming a plurality ofelectrodes outside the outer perimeter of the resonator, wherein theplurality of electrodes are not in physical contact with the outerstiffener ring, and wherein a gap is between each electrode and theouter stiffener ring.

In another aspect the gap is filled with a gas or a vacuum.

In another aspect the method further comprises forming a plurality ofinternal electrodes, wherein each internal electrode is located betweena curved spring and another curved and the at least one inner stiffenerring, or between a curved spring and another curved and the anchor, orbetween a curved spring and another curved and the outer stiffener ring,wherein the plurality of inner electrodes are not in physical contactwith the curved springs, the inner stiffener ring, the anchor or theouter stiffener ring, and wherein a gap is between each inner electrodeand adjacent curved springs, the at least one inner stiffener ring, theanchor and the outer stiffener ring.

In another aspect the outer stiffener ring has a width greater than awidth of each of the curved springs.

In another aspect the plurality of curved springs comprise a pluralityof convex springs coupled to the outer stiffener ring and pointingtowards the anchor.

In another aspect the plurality of curved springs comprise a pluralityof convex springs coupled to the anchor and pointing towards the outerstiffener ring.

In another embodiment disclosed herein, a method of providing aresonator comprises providing a wafer comprising an insulator withbackside wafer on one side of the insulator and front side wafer onanother side of the insulator, depositing and patterning front sidemetal on the front side wafer, patterning the front side wafer to exposethe insulator and to form an anchor, an outer stiffener ring on an outerperimeter of the resonator, and a plurality of curved springs betweenthe anchor and the outer stiffener ring, removing a portion of theinsulator to release a resonant portion of the resonator from thebackside wafer, and leaving an anchor portion of the resonator attachedto the backside wafer.

In one aspect the frontside wafer comprises Si, quartz, or SiC, and thebackside wafer comprises Si, quartz, or SiC.

These and other features and advantages will become further apparentfrom the detailed description and accompanying figures that follow. Inthe figures and description, numerals indicate the various features,like numerals referring to like features throughout both the drawingsand the description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B show a top and a tilted view, respectively, of aFlower-of-life Vibratory Gyroscope (FVG) resonator design in accordancewith the present disclosure;

FIG. 2 shows another FVG resonator design with stiffeners having auniform pitch or uniform increase in diameter from one stiffener toanother in accordance with the present disclosure;

FIG. 3A shows a FVG resonator with peripheral electrodes, and FIG. 3Bshows an expanded view of a portion of FIG. 3A in accordance with thepresent disclosure;

FIG. 4A shows a FVG resonator with both peripheral electrodes andinternal electrodes, and FIG. 4B shows an expanded view of a portion ofFIG. 4A in accordance with the present disclosure;

FIGS. 5A, 5B, 5C and 5D show a process flow for making a Flower-of-lifeVibratory Gyroscope (FVG) resonator in accordance with the presentdisclosure;

FIG. 6 shows a graph of the quality factor limited by thermo-elasticdamping (QTED) and resonance frequency of the Flower-of-life VibratoryGyroscope (FVG) compared with prior art Disk Resonator Gyroscopes (DRGs)in accordance with the present disclosure;

FIG. 7A shows a FVG resonator without any inner stiffener, FIG. 7B showsa FVG resonator having a Sun Burst design, FIG. 7C shows a FVG resonatorhaving an Inverse Sun Burst design, and FIGS. 7D, 7E and 7F show FVGresonator designs corresponding to FIGS. 7A, 7B and 7C and having awider outside ring in accordance with the present disclosure;

FIG. 8 shows a graph of QTED vs frequency for FVG resonator designshaving different ring widths (RW) in accordance with the presentdisclosure; and

FIG. 9 shows a FVG resonator design illustrating clockwise andcounter-clockwise springs in accordance with the present disclosure.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth toclearly describe various specific embodiments disclosed herein. Oneskilled in the art, however, will understand that the presently claimedinvention may be practiced without all of the specific details discussedbelow. In other instances, well known features have not been describedso as not to obscure the invention.

The present disclosure describes a high-Q (Quality Factor)Micro-Electro-Mechanical Systems (MEMS) silicon Flower-of-life VibratoryGyroscope (FVG) resonator. In the following, reference to an FVGincludes the FVG resonator.

Due to its symmetry, the FVG structure has a family of frequency-matched{cos/sin}(N*theta) vibration modes, where theta is the circumferentialdirection around the perimeter of the device and N is the mode number.N=1, N=2, N=3, N=4, etc. are mode numbers of interest for gyroscopeapplications, and N=2 is typical mode for a gyroscope application. Thesetypes of modes are ideal for a symmetric Coriolis vibratory gyroscope,because the Coriolis effect can efficiently transfer energy between afrequency-matched N-mode pair during rotation, providing a means tosense rotation. Further, the symmetry of the FVG structure means that,except for the N=1 mode, the centers of mass of the vibratory modesremain at the center of the structure and they inherently rejectacceleration. This is important since it is desirable to sense rotationrather than other effects such as acceleration.

The FVG resonator design allows deformation of its structure withouttwisting to reduce strain-induced thermal gradients, resulting in a highthermoelastic damping limited quality factor (QTED). The QTED for theFVG may be greater than 150,000. If the FVG resonator includescross-linked FVG springs, the effective stiffness of the FVG is enhancedwhile the mass is reduced compared to the prior art disk resonatorgyroscopes (DRGs). With cross-linked FVG springs, a high N=2 moderesonance frequency of greater than 30 kHz can be achieved, which ismore than twice the typical vibration frequencies of similar QTEDsilicon gyro structures, such as disk resonator gyroscopes (DRGs).Higher resonance frequency allows the gyroscope to operate without beingaffected by typical vibration environments encountered in manyapplications, which are typically less than 10 kHz. In addition, FVGswith thicknesses of 350 um (micrometers) or more may have reducedacceleration sensitivity, up to 50,000 Gs in any acceleration direction,compared to the prior art. The FVG design has a much higherelectrostatic frequency tuning range due to a lower mass compared toprior art silicon gyro designs, which has the benefit of cancellingfrequency splits caused by fabrication defects, vibration, and thermaleffects. In addition, a frequency tuning range can be achieved for theFVG through dynamic electrical means rather than static mechanicaltrimming. Further, by increasing the ring width for the whole structure,the FVG design may have a high adiabatic QTED since a wider ring widthof greater than 100 um has a resonance frequency greater than 100 kHz.The FVG provides a high-Q silicon vibratory gyroscope and resonatorstructure in frequency ranges previously not thought to be possible.

One object of the present disclosure is to enable the design of high-QMicro-Electro-Mechanical Systems (MEMS) silicon Coriolis vibratorygyroscopes (CVGs). Prior art CVGs include silicon disk resonatorgyroscopes (DRGs) with resonance frequencies around 14 kHz and Q-factorsof around 80,000. Due to their natural resonance frequency of around 14kHz, Si-DRGs may not operate well under harsh vibration and thermalconditions. The lower bound of the FVG resonance frequency is near 35kHz, which is more than double that of the typical DRG vibrationfrequency, so the FVG performance is not affected by typical vibrations.Prior art DRGs need vibration and thermal isolation mechanisms toachieve same bias stability. Also, the FVG may have a 155,000 Q-factor,which is 2 to 2.5 time that obtained by prior art DRGs. The upper boundof a FVG Q-factor may only be limited by thermoelastic dissipation(TED). The FVGs of the present disclosure are significantly lesssensitive to vibration and shock, and their tuning capability means thatthey can be tuned to accommodate any temperature induced drift.

The MEMS Flower-of-life Vibratory Gyroscope (FVG) is so called due toits geometry, as shown, for example in FIGS. 1A and 1B. The FVG has ahigh thermal elastic damping quality factor (QTED) and a high anchorquality factor (Qanchor), low acceleration sensitivity, a high frequencytuning range and higher resonance frequency than prior art DRGs thathave typical resonance frequencies of only about 10-15 kHz.

The Flower-of-life Vibratory Gyroscope (FVG) is so-called due to thecurved springs formed in the geometric flower-of-life pattern. Thepattern is produced by the overlapped curved springs that form theoutline of common leaf shapes. The common leaf shapes include but notlimited to linear, elliptical, oval, ovate, deltoid, cordate, oblong,rhomboid, obovate, oblanceolate, orbicular, lanceolate, reniform,spathulate, or combinations thereof. The leaf shapes must be symmetricaland symmetrically arranged around the anchor. The radial balance of theplurality of curved springs provide rotational symmetry about a centeraxis with N fold symmetry, where N is a positive integer.

The FVG resonator 10 shown in FIG. 1A has an anchor 12, springs 14 andstiffener rings 16. The anchor 12 is a solid cylinder at the center ofthe gyro 10. A silicon FVG resonator design may have an 8 mm outerdiameter and a 2 mm anchor diameter, although the outer diameter andanchor may have other dimensions. In FIG. 1A, 6 sets of stiffener rings16 are shown, including the outer perimeter 17, each having a ring widthof 10 um and a thickness of 350 um and an aspect ratio of 1:35, wherethe aspect ratio is the ratio of the width to the thickness. Thethickness of the stiffener rings 16 is best understood as the distancebetween a top 18 of the FVG and a bottom 20 of the FVG, as shown in thetilted view in FIG. 1B, and also shown in FIG. 5D. The thickness of theFVG 10, including the springs 14, may be the same as the thickness ofthe stiffener rings 16. The ring width is the dimension of the stiffenerring 16 orthogonal to the thickness dimension. The springs 14 areconnected to the anchor 12 and to each stiffener ring 16 including thestiffener ring 16 on the outer perimeter 17. The springs 14 are curved.In the FVG of FIGS. 1A and 1B, there are sixteen pairs of springs 14.Each pair of springs 14, such as the pair of springs 22 and 24, are inthe form of a circle, which has its circumference not entirely closedbecause of the intersection of springs 14 with the anchor 12. Each pairof springs 14 includes a spring 22 having a convex curvature, and aspring 24 having a concave curvature. Alternatively, the FVG may bedescribed as having pairs of springs, such as the pair of springs 22 and23, shown in FIG. 1A, having a clockwise curvature 102 and having acounter-clockwise curvature 100, respectively, as shown in FIG. 9. Eachsuch pair of springs in FIGS. 4A, 4B, 7A and 7D also may be described asa spring 102 having a clockwise curvature 102, which follows a pathoriginating at the anchor and curving in a clockwise direction towardthe outer ring 17, and a spring 100 having a counter-clockwise curvature100, which follows a path originating at the anchor and curving in acounter-clockwise direction toward the outer ring 17, as shown in FIG.9.

If inner stiffener rings 16 are included between the stiffener ring onthe outer perimeter 17 (the outer stiffener ring) and the anchor 12,then the curved springs 14 are arranged between the anchor 12 and theouter stiffener ring 17 such that a respective spring 14 having a convexcurvature intersects a respective spring 14 having a concave curvatureand respective inner stiffener ring 16 at a same location on therespective inner stiffener ring 16.

The number of pairs of springs 14 may be any number and the spacingbetween the pairs of springs 14 may vary from that shown in FIGS. 1A and1B. The springs 14 shown in FIGS. 1A and 1B have a rotational symmetryabout a center axis with an 8 times N fold of symmetry, where N is apositive integer. The springs 14 may have an aspect ratio ranging from1:500 to 50:1, where the aspect ratio is the ratio of the width to thethickness.

The diameter of the outer perimeter 17 of the FVG may range from 1-20millimeters (mm), the anchor 12 diameter may range from 0.1-10 mm, thestiffener ring 16 width may range from 1-500 micrometers (um), and thedevice thickness, which is the same as the stiffener ring 16 thicknessmay range from 10-500 um. The aspect ratio of the stiffener ring 16 maybe from 1:500 to 50:1, where the aspect ratio is the ratio of the widthto the thickness. The number of stiffener rings 16 can be 1-20. In thecase of only one stiffener ring 16, the stiffener ring 16 wouldpreferably be on the outer perimeter 17 of the FVG resonator 10. Therotational symmetry of the FVG may be any positive integer (e.g., 1, 2,3, . . . etc.).

The stiffener rings 16 are concentric with another and concentric withthe anchor 12. The stiffener rings 16 may be located so that thestiffener rings 16 intersect the springs 14 at locations where onespring 14 intersects another spring 14, to stiffen the springs. Springstiffeners or stiffener rings 16 are important for gyro performance atlow frequency (<50 kHz) since the stiffener rings 16 increase thestiffness of the gyro structure with only a slight increment of mass,resulting in a high resonance frequency and a high frequency tuningrange. Increasing the number of stiffener rings 16 can reduce anchor andTED loss. The location of each stiffener is preferably chosen tominimize any extra intersections for heat loss.

The FVG resonator design is such that all the springs 14 and stiffeners16 are joined seamlessly, unlike prior art DRGs that may have a“dog-bone” shape as a connector between rings, as shown in FIG. 1A ofU.S. Pat. No. 7,581,443, issued Sep. 1, 2009. The prior art DRG dog-boneconnectors prevent the rings of the DRG from deforming freely into an N2elliptical mode shape. Therefore prior art DRG rings twist duringresonance, and twisting of the DRG rings generates hot and cold spots,causing heat loss in the DRG structures. The FVG spring 14 designeliminates this problem.

As shown in FIG. 2, the curvature of the springs 14 can be varied sothere is a uniform pitch 30 between the concentric stiffener rings 16,which distributes mass uniformly in the radial direction. Also couplingbetween the anchor 12 and the FVG resonance structure can be reduced bymodifying the curvature of the springs 14 so that near the anchor 12 acurved triangle formed by the intersection of the springs 14 is a widerangle rather than a narrow angle.

FIGS. 3A and 3B, which is an expanded view of a portion of FIG. 3A, showa FVG resonator with peripheral electrodes 34. The peripheral electrodes34 are connected to metal contacts 35 and are not in physical contactwith the FVG outer diameter or the outer stiffener 16. A gap 36 isbetween the FVG and the peripheral electrodes 34 and may be filled witha gas, such as air, or the gap 36 may be a vacuum. An electrode set gap37 is between the peripheral electrodes 34 and ground electrodes 38 andmay be filled with a gas, such as air, or the electrode set gap 37 maybe a vacuum. The dimension of the electrode set gap 37 may be greaterthan or equal to the gap 36.

FIG. 4A and FIG. 4B, which is an expanded view of a portion of FIG. 4A,show a FVG resonator with both peripheral electrodes 34 and internalelectrodes 40. Similarly to the description for FIGS. 3A and 3B, theperipheral electrodes 34 are connected to metal contacts 35 and are notin physical contact with the FVG outer diameter or the outer stiffener16, and a gap 36 is between the FVG and the peripheral electrodes 34 andmay be filled with a gas, such as air, or the gap 36 may be a vacuum. Anelectrode set gap 37 is between the peripheral electrodes 34 and groundelectrodes 38 and may be filled with a gas, such as air, or theelectrode set gap 37 may be a vacuum. The dimension of the electrode setgap 37 may be greater than or equal to the gap 36. The internalelectrodes 40 are in spaces between the springs 14 and the stiffenerrings 16. Gaps 42 are between each internal electrode 40 and anyadjacent springs 14 or stiffener ring 16. The gaps 42 may be filled witha gas, such as air, or the gaps 42 may be a vacuum.

The FVG resonator fabrication process is shown in FIGS. 5A, 5B, 5C and5D. FIGS. 5A, 5B, 5C and 5D show a fabrication example for asilicon-on-insulator (SOI} configuration; however rather than silicon,quartz or SiC can be used. Also, the SiO₂ and Au shown may be anyappropriate insulator or metal, respectively. It should also beunderstood that the etching steps may be more broadly be stated aspatterning.

First, as shown in FIG. 5A, a backside alignment target 50 is formed bypatterning silicon (Si) 54 on the backside of a wafer, which may be asilicon-on-insulator (SOI) wafer. The SOI wafer has backside silicon 54,which is used as a handle, and frontside Si 60. Both the frontside Si 54and the backside Si 60 are on insulator 56. Then backside metal 52 maybe patterned and deposited. The backside metal 52 is for die attachmentto a Leadless Chip Carrier (LCC) package.

Then, as shown in FIG. 5B, a front side alignment target 62 is etched inSi 60 on the front side of the SOI wafer. Next front side metal ispatterned and deposited for electrical contacts 35, some of which arecoupled to the peripheral electrodes 34.

Then, as shown in FIG. 5C, the FVG resonator 10 is formed by DeepReactive-Ion Etching (DRIE) of the frontside Si 60, and exposing theburied insulator 56, which may be silicon dioxide (SiO₂).

Next, as shown in FIG. 5D, a portion 66 of the buried insulator 56 isremoved by using a hydrofluoric (HF) acid undercut to release the FVGstructure 10 from the Si handle 54. Another portion 68 is left intactbetween the resonator structure 10 and the backside Si 54 of the SOIwafer to provide mechanical support.

The Flower-of-life vibratory gyroscope using the FVG resonator hasbetter gyro performance than prior art DRGs, in terms of quality factorsQTED and Qanchor and less acceleration sensitivity. The FVG not only hasbetter performance, but also has a higher N=2 mode resonance frequency,allowing operation in harsh vibration environments.

FIG. 6 shows that a FVG resonator may achieve a quality factor (Q) of155,000 (1.55E5) at a frequency of 35 kHz, as shown by triangle 70. TheFVG resonator is 2.5 times higher than the prior art DRGs in terms ofN=2 mode resonance frequency, and 2.0 times the prior art in terms ofthermo-elastic damping quality (QTED). The triangle 70 marks the QTEDfor a FVG design having the following geometry dimensions: a 10 umstiffener ring width, a 8 mm outer diameter, a 2 mm anchor diameter, and5 stiffener rings 16, as shown in FIGS. 1A and 1B. The circles in FIG. 6represent prior art DRG designs with the black circle 72 marking thebest to date prior art DRG design. Compared with the prior art DRGs, theFVG design enables a high Q silicon MEMS gyroscope to operate at afrequency greater than 20 kHz without compromising other performanceaspects, including vibration insensitivity and electrical frequencytuning range.

Other FVG variations are shown in FIGS. 7A to 7F. FIG. 7A shows a FVGwithout any stiffeners 16, except for the outer ring 16. FIG. 7B shows aFVG with a socalled sun burst spring 14 pattern between the outer ring16 and the anchor 12, and FIG. 7C shows a FVG with a socalled inversesun burst spring 14 pattern between the outer ring 16 and the anchor 12.The sun burst spring pattern of FIG. 7B has convex springs pointingtoward the anchor 12, and the inverse sun burst spring pattern of FIG.7C has convex springs pointing away from the anchor 12. FIGS. 7D, 7E and7F show FVG designs that are the same as FIGS. 7A, 7B and 7C,respectively, except that the outer ring 16 on the outer perimeter 17 inFIGS. 7D, 7E and 7F has a wider ring width relative to the width of thesprings 14. In FIGS. 7A, 7B and 7C the outer ring 16 and the springs 14have the same width.

The FVG without an inner stiffener has a unit cell of a diamond shapewith curve edges, as shown in FIG. 7A. Sun Burst designs and Inverse Sunburst designs have unit cells having a curved triangle shape, like apaper fan, as shown in FIGS. 7B and 7C. The dome part of each unit cellpoints towards the center of the resonator structure for Sun Burstdesigns, as shown in FIGS. 7B and 7E, but the dome part of each unitcell points away from the center of the resonator structure for InverseSun Burst designs, as shown in FIGS. 7C and 7F.

Ring width, stiffener ring number, radius of curvature, and inner andouter diameter are the key design parameters to understand therelationship to quality factor, acceleration sensitivity, and frequencytunability of the MEMS gyroscope.

FIG. 8 shows a graph of QTED vs frequency for FVG designs for variousring and spring widths. For the results in FIG. 8, both the springs andthe outer stiffener ring are configured to have the same thickness andboth are increased from 10 um to 400 um. Based on a COMSOL simulationwith thermo-elastic damping, FIG. 8 shows that a high adiabatic QTED canbe achieved for the FVG by increasing the width of the springs 14, forexample to 300 um, without the need to add any stiffeners, other thanthe outside ring 16. As shown in FIG. 8, a FVG having springs 14 with awidth of 400 um, as shown by triangle 80, has a higher QTED andresonance frequency than a FVG having springs 14 with a width of 300 um,as shown by triangle 82. Also, a FVG having springs 14 with a width of300 um has a higher QTED and resonance frequency than a FVG having asprings with a width of 10 um, as shown by triangles 82 and 84,respectively. Also shown is the QTED and resonance frequency for a priorart disk resonator gyroscope (DRG), as shown by black dot 86, which hasa much lower QTED and resonance frequency than that achieved by the FVGdesigns.

Having now described the invention in accordance with the requirementsof the patent statutes, those skilled in this art will understand how tomake changes and modifications to the present invention to meet theirspecific requirements or conditions. Such changes and modifications maybe made without departing from the scope and spirit of the invention asdisclosed herein.

The foregoing Detailed Description of exemplary and preferredembodiments is presented for purposes of illustration and disclosure inaccordance with the requirements of the law. It is not intended to beexhaustive nor to limit the invention to the precise form(s) described,but only to enable others skilled in the art to understand how theinvention may be suited for a particular use or implementation. Thepossibility of modifications and variations will be apparent topractitioners skilled in the art. No limitation is intended by thedescription of exemplary embodiments which may have included tolerances,feature dimensions, specific operating conditions, engineeringspecifications, or the like, and which may vary between implementationsor with changes to the state of the art, and no limitation should beimplied therefrom. Applicant has made this disclosure with respect tothe current state of the art, but also contemplates advancements andthat adaptations in the future may take into consideration of thoseadvancements, namely in accordance with the then current state of theart. It is intended that the scope of the invention be defined by theClaims as written and equivalents as applicable. Reference to a claimelement in the singular is not intended to mean “one and only one”unless explicitly so stated. Moreover, no element, component, nor methodor process step in this disclosure is intended to be dedicated to thepublic regardless of whether the element, component, or step isexplicitly recited in the Claims. No claim element herein is to beconstrued under the provisions of 35 U.S.C. Sec. 112, sixth paragraph,unless the element is expressly recited using the phrase “means for . .. ” and no method or process step herein is to be construed under thoseprovisions unless the step, or steps, are expressly recited using thephrase “comprising the step(s) of . . . .”

What is claimed is:
 1. A resonator comprising: an anchor; an outerstiffener ring on an outer perimeter of the resonator; at least oneinner stiffener ring concentric with the outer stiffener ring; and aplurality of curved springs coupled to the anchor and to the outerstiffener ring; wherein each of the plurality of curved springs arecoupled to the at least one inner stiffener ring; wherein the outerstiffener ring has a first diameter that is greater than a seconddiameter of the inner stiffener ring; and wherein each of the pluralityof curved springs comprises a convex spring.
 2. The resonator of claim 1wherein: the outer stiffener ring has a first diameter; and the anchoris concentric with the outer stiffener ring and has a second diameterless than the first diameter.
 3. The resonator of claim 1 wherein: theplurality of curved springs have a rotational symmetry about a centeraxis with an N fold of symmetry, where N is a positive integer.
 4. Theresonator of claim 1 further comprising: a plurality of inner stiffenerrings each concentric with the outer stiffener ring; wherein a pitchbetween each adjacent inner stiffener ring, or between the outerstiffener ring and a respective inner stiffener ring adjacent to theouter stiffener ring, or between the anchor and a respective innerstiffener ring adjacent to the anchor is the same.
 5. The resonator ofclaim 1 further comprising: a plurality of electrodes outside the outerperimeter of the resonator; wherein the plurality of electrodes are notin physical contact with the outer stiffener ring; and wherein a gap isbetween each electrode and the outer stiffener ring.
 6. The resonator ofclaim 1 further comprising: a plurality of internal electrodes; whereineach internal electrode is located between a curved spring and anothercurved spring and the at least one inner stiffener ring, or between acurved spring and another curved spring and the anchor, or between acurved spring and another curved spring and the outer stiffener ring;wherein the plurality of internal electrodes are not in physical contactwith the curved springs, the inner stiffener ring, the anchor or theouter stiffener ring; and wherein a gap is between each internalelectrode and adjacent curved springs, the at least one inner stiffenerring, the anchor and the outer stiffener ring.
 7. The resonator of claim1 wherein: the outer stiffener ring has an aspect ratio ranging from1:500 to 50:1; and each of the curved springs of the plurality of curvedsprings has an aspect ratio ranging from 1:500 to 50:1.
 8. A resonatorcomprising: an anchor; an outer stiffener ring on an outer perimeter ofthe resonator; a first plurality of first curved convex springs, eachhaving a first end and a second end coupled to the outer stiffener ring;and a second plurality of second curved convex springs, wherein eachrespective second curved convex spring has a first end coupled to afirst curved convex spring and a second end coupled to a different firstcurved convex spring; wherein the first plurality of first curved convexsprings point toward the anchor; and wherein the second plurality ofsecond curved convex springs point toward the anchor.
 9. A resonatorcomprising: an anchor; an outer stiffener ring on an outer perimeter ofthe resonator; a first plurality of first curved convex springs, eachrespective first curved convex spring pointing toward the outerstiffener ring and coupled to the outer stiffener ring at a pointbetween a first end and a second end of the respective first curvedconvex spring; and a second plurality of second curved convex springs,each respective second curved convex spring pointing toward the outerstiffener ring and coupled to a respective first end of a respectivefirst curved convex spring and coupled to a respective first end of adifferent respective first curved convex spring.
 10. A resonatorcomprising: an anchor; an outer stiffener ring on an outer perimeter ofthe resonator; and a plurality of curved springs coupled to the anchorand to the outer stiffener ring; wherein each of the plurality of curvedsprings comprises a convex spring; and wherein the plurality of curvedsprings is configured in a flower-of-life pattern by overlapping curvedsprings to form outlines of leaf shapes; wherein the outlines of leafshapes formed comprise linear, elliptical, oval, ovate, deltoid,cordate, oblong, rhomboid, obovate, oblanceolate, orbicular, lanceolate,reniform, or spathulate outlines, or combinations thereof; wherein theoutlines of leaf shapes formed are symmetric and symmetrically arrangedaround the anchor; and wherein the flower-of-life pattern has arotational symmetry about a center axis with N fold of symmetry, where Nis a positive integer.
 11. The resonator of claim 10 wherein: the outerstiffener ring has a first diameter; and the anchor is concentric withthe outer stiffener ring and has a second diameter less than the firstdiameter.
 12. The resonator of claim 10 further comprising: at least oneinner stiffener ring concentric with the outer stiffener ring; whereinthe plurality of curved springs are coupled to the at least one innerstiffener ring; and wherein the outer stiffener ring has a firstdiameter that is greater than a second diameter of the at least oneinner stiffener ring.
 13. The resonator of claim 10 further comprising:a plurality of inner stiffener rings each concentric with the outerstiffener ring; wherein a pitch between each adjacent inner stiffenerring, or between the outer stiffener ring and a respective innerstiffener ring adjacent to the outer stiffener ring, or between theanchor and a respective inner stiffener ring adjacent to the anchor isthe same.
 14. The resonator of claim 10 further comprising: a pluralityof electrodes outside the outer perimeter of the resonator; wherein theplurality of electrodes are not in physical contact with the outerstiffener ring; and wherein a gap is between each electrode and theouter stiffener ring.
 15. The resonator of claim 10 further comprising:a plurality of internal electrodes; wherein each internal electrode islocated between a curved spring and another curved spring and the atleast one inner stiffener ring, or between a curved spring and anothercurved spring and the anchor, or between a curved spring and anothercurved spring and the outer stiffener ring; wherein the plurality ofinternal electrodes are not in physical contact with the curved springs,the inner stiffener ring, the anchor or the outer stiffener ring; andwherein a gap is between each internal electrode and adjacent curvedsprings, the at least one inner stiffener ring, the anchor and the outerstiffener ring.